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IC 8919 



Bureau of Mines Information Circular/1983 




Guidelines for Siting 
Product-of-Combustion Fire 
Sensors in Underground Mines 



By C. D. Litton 




UNITED STATES DEPARTMENT OF THE INTERIOR 



Information Circular 8919 
1 

Guidelines for Siting 
Product-of-Combustion Fire 
Sensors in Underground Mines 

By C. D. Litton 




UNITED STATES DEPARTMENT OF THE INTERIOR 
James G. Watt, Secretary 

BUREAU OF MINES 
Robert C. Horton, Director 



This publication has been cataloged as follows: 




Litton, C. D. (Charles D.) 

Guidelines for siting product-of-combustion fire sensors in under- 
ground mines. 

(Information circular/ United States Department of the Interior, Bu- 
reau of Mines ; 8919). 

Includes bibliographical references. 
Supt. of Docs, no.: I 28.27:8919. 

1. Mine fires— Prevention and control. 2. Fire detectors— Location. 
3. Combustion gases. I. Title. II. Series: Information circular (United 
States. Bureau of Mines) ; 8919. 



[TN315] 



622s [622'. 8] 82-600343 






■Ok 



CONTENTS 



I 

4 
J- 



Page 



Abstract 1 

Introduction 2 

Spacing and siting guidelines 2 

Spacing 2 

Vertical placement 4 

Lateral placement 5 

Fire detection criterion 5 

Products of combustion 6 

Sensor spacing categories 7 

Category 1 mine entries 7 

Category 2 mine entries 7 

Category 3 mine entries 8 

Category 4 mine entries 8 

Sampling-type fire detectors 8 

Appendix A. — Derivation of low-flow sensor spacings 10 

Appendix B. — Derivation of tube traveltimes 12 

ILLUSTRATIONS 

1. Entry parameter (Ye) as a function of the entry height-to-width ratio (H/W) 3 

2. POC parameter (Y x ) as a function of the ratio of alarm threshold to produc- 

tion constant [(X a -X )/K x ] 3 

3. Spacing categories and appropriate spacing equations for mine entries 4 

TABLE 

1. Production constants for coal and wood 3 



GUIDELINES FOR SITING PRODUCT-OF-COMBUSTION FIRE 
SENSORS IN UNDERGROUND MINES 

By C. D. Litton 1 



ABSTRACT 

This Bureau of Mines report presents a set of guidelines for determin- 
ing the distribution of product-of-combustion fire sensors in under- 
ground mines. Sensor spacing is defined in terms of sensor alarm 
threshold, ventilation flow rate, and mine entry dimensions. Sensor 
spacing guidelines are presented for detection of fires from two primary 
combustibles, coal and wood, which are common to the majority of under- 
ground mines. The guidelines are based on data from full-scale and 
intermediate-scale fire tests conducted by the Bureau of Mines. 

— . 

Supervisory physical scientist, Pittsburgh Research Center, Bureau of Mines, 
Pittsburgh, Pa. 



INTRODUCTION 



A major goal of the Bureau of Mines 
safety research program is to improve the 
degree of safety afforded underground 
miners. Rapid and reliable detection of 
mine fires can contribute to this goal by 
improving miners' chances for escape dur- 
ing actual fire emergencies. 

It is apparent that the use of sensi- 
tive and reliable product-of-combustion 
(POC) fire sensors in underground mines 
is increasing, owing primarily to the 
greater availability of such sensors, as 
well as an added awareness of the need 
for rapid and reliable underground fire 
detection systems. As the use of such 
sensors grows, the required distribution 
of these sensors within mine entries will 
need to be determined in order to provide 
realistic and adequate fire detection. 
Previous Bureau reports 2 have discussed 



this problem and outlined the various 
parameters involved. 

This report summarizes the previous 
data and presents subsequent guidelines 
for determining POC fire sensor distribu- 
tions within mine entries. These guide- 
lines may be easily used by those respon- 
sible for either designing or approving 
the design of POC fire detection systems 
in underground mines. 

It is not the intent of this report to 
suggest or recommend specific fire sen- 
sors or sensing systems. Rather, the 
report proposes a strategy for determin- 
ing the most effective distribution of 
whatever sensors are selected. It is 
important that one using these guidelines 
know in advance the type of sensor to be 
used and its characteristics. 



SPACING AND SITING GUIDELINES 



For convenience, the spacing and siting 
guidelines for POC fire sensors in under- 
ground mines are presented first, along 
with instructions for their general use. 
Explanatory material, on which the guide- 
lines are based, can be found in the sec- 
tions that follow. 



2 Litton, C. D. Product-of -Combust ion 
Fire Detection in Mines. Paper in Under- 
ground Metal and Nonmetal Mine Fire Pro- 
tection. Proceedings: Bureau of Mines 
Technology Transfer Seminars, Denver, 
Colo., Nov. 3, 1981, and St. Louis, Mo., 
Nov. 6, 1981. BuMines IC 8865, 1981, 
pp. 28-48. 

Litton, C. D., M. Hertzberg, and A. L. 
Furno. Fire Detection Systems in Con- 
veyor Belt Haulageways. BuMines RI 8632, 
1982, 26 pp. 

. The Growth, Structure, and De- 
tec tability of Fires in Mines and Tun- 
nels. Proc. 18th Internat. Symp. on Com- 
bustion, Waterloo, Ontario, Canada, Aug. 
17-25, 1980. The Combustion Institute, 
Pittsburgh, Pa., 1981, pp. 633-639. 



SPACING 

To determine the appropriate spacing 
between POC fire sensors within a 
mine entry, these steps should be 
followed: 



1. Determine the average 
(H) and width (W) . 



entry height 



2. Take the ratio of height to width 
(H/W) and, from figure 1, determine the 
appropriate value for the entry parameter 
(Ye). 

3. Determine the type of sensor to be 
used (CO, CO2 , or smoke) and its alarm 
threshold (X a ); that is, the POC concen- 
tration that will activate the sensor 
alarm. 

4. Determine the primary combustible 
within the entry (either coal or wood) 
and, from table 1, select the production 
constant (K x ) for the product to be 
detected. 



45 



40 



LU 

k 35 

UJ 

I- 
LJ 
2 
< 

< 
Q. 

E 30 



UJ 



25 



20 



1 1 1 1 1 i r 



- f Sr- 



y E =22.7(3.05) a875H/ w 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 °o 

ENTRY HEIGHT-TO-WIDTH RATIO ( H / w ) 



FIGURE 1. - Entry parameter (y E ) as a func- 
tion of the entry height-to-width ratio (H/W). 



TABLE 1. - Production constants for coal 
and wood 



K, 



1 



K C0 

K co 2 

K SMP 



K 



SMP 



POC concen- 
tration units 



PPm 

PPm 

particles per 

cm 3 . 
mg/m 3 



Coal 



7.2 x 



1.10 

6.70 

10 4 

0.45 



Wood 



2.5 x 



0.95 

6.90 

10 5 

0.30 



SMP Smoke particles. 
Subscript indicates sensor type. 



5. Determine (or estimate) the aver- 
age background level (X ) of the product 
to be detected. 

6. Subtract X from X a and divide the 
result by the appropriate K x -value. 

7. From figure 2, determine the value 
of the POC parameter (Y x ) at the value of 

x a -x 



K> 



- defined in step 6. 




_L 



_L 



10 



20 30 40 50 



60 70 



80 



FIGURE 2. - POC parameter (y x ) as a func- 
tion of the ratio of alarm threshold to produc- 
tion constant [(X^-XJ/KJ. 

8. Determine the average ventilation 
velocity (Vf), in feet per minute, within 
the entry and, in figure 3, draw a ver- 
tical line at this velocity parallel to 
the y-axis. 

9. Multiply H by W to determine the 
average entry cross-sectional area (A) 
and, in figure 3, draw a horizontal line 
at this A-value parallel to the x-axis. 

10. The point of intersection of the 
vertical and horizontal lines in figure 3 
defines the appropriate spacing category 
to be used for this entry, and the ap- 
propriate spacing equation. 

For illustrative purposes, consider the 
following example. 

1. H = 6 ft; W = 20 ft. 

2. From figure 1, at H/W = 6/20 
= 0.3, ye = 30.4. 

3. Sensor type: CO; alarm threshold 
(X a ) = 20 ppm. 



oo 




At 







Category 2 



A-l4v/'(x E -y x ) 



Category I 
A-(v f A)^( XE - Xx ) 



00 200 300 400 500 
ENTRY VENTILATION VELOCITY (v f ),ft/min 



^V 



oo 



FIGURE 3. - Spacing categories and appropriate spacing equations for mine entries. 

i x < (vfA) 1 / 2 (Te-Yx) 
< 190 (30.4 - 19.0) 



4. Primary combustible: coal; from 
table 1, Kqq for coal = 1.10. 



5. Entry background CO level (X ) 
= 4 ppm. 

6. (X a -X o )/K C0 = 14.5. 

7. From figure 2, at (X a -X o )/Kc 
= 14.5, Y x = 19.0. 

8. Average entry ventilation velocity 
(v f ) = 300 ft/min. 

9. Average entry cross section (A) 
= H x w = 6 x 20 = 120 ft 2 . 

10. The point of intersection of the 
Vf-vertical line and the A-horizontal 
line, in figure 3, falls within cate- 
gory 1. For category 1, the appropriate 
sensor spacing equation is 



< 2,166 ft. 

This is the maximum recommended spacing 
between these sensors in this entry. 

VERTICAL PLACEMENT 

Because the hot gases from a fire will 
rise owing to buoyancy forces, combustion 
products will initially be stratified 
near the roof of an entry. As this 
stratified gas layer moves away from the 
fire, the resultant cooling and dilution 
will eventually produce a well-mixed flow 
of combustion products. Data from full- 
scale fires indicate that some degree of 
stratification can exist at distances of 



hundreds 
fire. 



of feet from the source of the 



Because of this eff 
sors should be located 
tance from the entry 
exceed 25% of the ave 
For example, in an ent 
6 ft, the maximum dist 
at which a POC sensor 
is 1-1/2 ft. This ref 
of the actual sampli 
detector used. 



ect, POC fire sen- 
at a vertical dis- 
roof that does not 
rage entry height, 
ry with a height of 
ance from the roof 
should be located 
ers to the location 
ng intake of the 



LATERAL PLACEMENT 

In general, the point of origin of a 
fire is quite unpredictable. It may 



occur along the floor, ribs, or roof of 
an entry. In order to provide optimum 
protection, it is recommended that the 
fire sensors be located within 2 ft of 
the approximate midpoint of the entry. 

For entries in which the point of ori- 
gin of the fire can be better estimated 
(such as a belt entry), the sensors 
should be located in such a manner that 
they provide for the estimated best cov- 
erage of that entry. As an example, in a 
belt entry where the conveyor is on one 
side of the entry, it would be more 
judicious to locate the sensors above the 
centerline of the belt conveyor than to 
locate them in the middle of the entry. 



FIRE DETECTION CRITERION 



The basis for development of POC fire 
sensor spacing guidelines is the perfor- 
mance of a series of ideal 160° F heat 
sensors spaced at intervals of 10 ft 
within an underground mine entry. The 
estimated alarm times for this ideal 
thermal system define the detection 
criterion for POC fire sensors: Any POC 
fire-sensing system must have an alarm 
time less than or equal to this thermal 
alarm time. 



where T a = maximum downstream air tem- 
perature, °F, at a dis- 
tance I downstream; 

T = ambient air temperature, °F; 

Qf = fire heat release rate, 
Btu/min; 

p = density of air = 0.075 lb/ 
ft 3 ; 



The data obtained from full-scale mine 
fires 3 are used in the following para- 
graphs to estimate the fire sizes and 
alarm actuation times for the ideal 
160° F heat sensors with spacing inter- 
vals of 10 ft. 

Temperature data obtained during full- 
scale mine fires 4 indicate that the maxi- 
mum downstream air temperature at a dis- 
tance & is related to the heat release 
rate of the fire, the entry ventilation 
velocity, and the entry dimensions by the 
equation 



Q f = p c p v f A I2JE0 (0.305 I) 



1.75 H/W 



, (1) 



-"Second and third works cited in foot- 
note 2. 

4 Second work cited in footnote 2. 



and 



Cp = heat capacity of air = 0.26 
Btu/(lb'°F); 

Vf = ventilating air velocity, 
f t/min; 



I = distance from fire to down- 
stream thermal sensor, ft; 

H = entry height, ft; 

W = entry width, ft; 

A = entry cross-sectional area 
(H x W), ft 2 . 



Using equation 1, the detection crite- 
rion is developed as follows. The maxi- 
mum downstream distance is set equal to 
10 ft; T a equals 160° F; and T is 
assumed to have a value of 65° F. From 



equation 1, the fire size at which the 
maximum air temperature reaches 160° F at 
a distance of 10 ft downstream becomes 

Q T = 0.206 v f A (3.05) 1 ' 75 H/w , (2) 

where the subscript T denotes the fire 
size at the time of thermal alarm. 

From data previously reported, 5 the 
rate at which the fire size increases, 
from the instant of flaming ignition, is 
given by 

Q f = 4.0 x 10" 4 v f 2 t 2 , (3) 

where t is the time, in minutes. 

By setting Q f = Q T and solving for t in 
equation 3, the time to thermal alarm 
(t T ) can be determined: 



t T = 22.7 (3.05) 



0.875 H/W (v f A) 1/2 



r f 



(4) 



Equations 2 and 4 define the approxi- 
mate fire size at time of alarm and the 
resultant alarm time for a series of 
ideal 160° F heat sensors spaced at in- 
tervals of 10 ft. Further, the 10-ft 
spacing is constant, independent of the 
entry dimensions. In essence, then, 
equations 2 and 4 define the fire size at 
alarm and the alarm time for ideal 160° F 
heat sensors within any entry; and for 
known values of H, W, and Vf , the actual 
fire sizes and times can be calculated. 



The criterion can be stated as follows: 
Any fire detection system installed 
within an entry of height H, width 
W, and ventilation velocity Vf must 
respond (alarm) in a time less than or 
equal to the time required for a series 
of ideal 160° F heat sensors spaced at 
10-ft intervals to respond if located 
in the same entry. This thermal re- 
sponse time, which serves as the basis 
for comparison, is defined in equa- 
tion 4. 

Since t T is a function of H and W, it 
is convenient to define a parameter, Ye» 
called the entry parameter, as 



Y E = 22.7 (3.05) - 875 H / w . 



(5) 



This parameter is plotted in figure 1 as 
a function of H/W. 

With this defined entry parameter, ty 
can be rewritten as 



t T = Y E 



(v f A) 



1/2 



(6) 



The following sections apply this de- 
tection criterion to the development of 
spacing guidelines for POC fire sensors 
in underground mines. This criterion can 
also be used to define spacings for heat 
sensors with alarm thresholds other than 
the assumed 160° F, through the use of 
equation 1. 



PRODUCTS OF COMBUSTION 



The quantity of any combustion product 
will increase as the fire size increases. 
In a ventilated mine entry, the bulk 
average increase in concentration for 
some product (X) is equal to the rate of 
generation of that product divided by the 
volumetric ventilation rate (simple dilu- 
tion). The equation that defines this 
bulk average concentration increase is 



where Xj = total concentration of prod- 
uct X; 

X = ambient background concen- 
tration of product X; 

Y x = quantity of X produced per 
mass of combustible con- 
sumed (the yield of X); 



X T -X - 



Of 



VfA 



(7) 



'Second work cited in footnote 2 



and H c = heat of combustion of the 
material burning. 

When X T equals the alarm threshold 
concentration (X a ), equation 7 can be 



rearranged to obtain the approximate fire 
size (Q x ) required to produce X a : 



H 



Q x = v f A ==£ (X a -X ). 



(8) 



By setting Qf = Q x in equation 3, the 
time at which the POC concentration will 
reach the alarm threshold (t x ) can be 
determined. 



t x = 50 



•°Gi 



(x a -x ) 



1 /2 ( Vf A) 1 / 2 
v f 



. (9) 



By setting the ratio Y x /H c equal to 
100 K x , equation 9 becomes 



tx . 5.0 Q*g*>) (Tf C; • (10) 

The parameter K x is defined as the pro- 
duction constant for product X and is 
also a function of the combustible that 
is burning. K x -values for the products 
CO, CO2 , and smoke particles (SMP) have 
been obtained from full-scale and 
intermediate-scale fire tests for both 
coal and wood 6 during flaming combustion 
and are listed in table 1. 



A second global parameter, Y x , called 
the POC parameter, is defined by the 
expression 



/, - 5.0' Xa x ° 



1/2 



(11) 



Y x is plotted in figure 2 as a function 
of (X a -X )/K x . When this parameter 
is inserted into equation 10, t x becomes 



tx = T x 



(v f A) 1 / 2 



(12) 



In order to satisfy the criterion of 
equation 6, the time available (t D ) for 
the transport of the alarm threshold con- 
centration level of product X from the 
fire origin to a sensor site is 



to - t T~ t x> 



(13) 



which, in terms of the two parameters, 
Ye and Y x , becomes 



1/2 



(v f AV^ , , 
tn = ^- L - L (Yf-Tx). 



(14) 



SENSOR SPACING CATEGORIES 



Because the entry cross sections of 
underground mines and the imposed entry 
ventilation rates can vary greatly, a 
single equation cannot be applied equi- 
tably for the spacing of all underground 
mine fire sensors. For this reason, the 
spacing guidelines are subdivided into 
four distinct categories of entry cross 
sections and ventilation flows. (These 
categories are shown in figure 3.) 

CATEGORY 1 MINE ENTRIES 

For any mine entry in which the entry 
cross section is <200 ft 2 , the entry 
ventilation flow is >50 ft/min, and the 
ratio A/vf is <2.0 f t 'min, the maximum 
sensor spacing is equal to 

H x < v f t D = (v f A) 1 / 2 (Ye-Yx)> (15) 

"First and second works cited in foot- 
note 2. 



where it is assumed that the combustion 
products are convected from the fire 
origin to the sensor site at a velocity 
equal to the average ventilation velocity 
in that entry. 

CATEGORY 2 MINE ENTRIES 

For any mine entry in which the entry 
cross section exceeds 200 ft^ and the 
ratio A/vf is <2.0 ft'min, to can be no 
greater than 

t D < (200/v f ) 1 / 2 (Ye-Y x )» (16) 

and the maximum sensor spacing no greater 
than 



* x < 14 v f 1/2 ( Ye -y x ). 



(17) 



8 



CATEGORY 3 MINE ENTRIES 

For any mine in which the ratio A/vf is 
i.O ft'min, regardless of entrj 
section, t D can be no greater than 

t D < (2) 1/2 (y E -T x ) = 1.4 (Y E -Y X )> (18) 



CATEGORY 4 MINE ENTRIES 

For any mine entry in which the venti- 
>2.0 ffmin, regardless of entry cross lation velocity is <50 ft/min, the maxi- 
mum sensor spacing is defined by 



£ x < 72 H 1/2 (y e -Y x ) 1/2 « 



(20) 



and the maximum sensor spacing no greater This expression is based upon a no-flow 



than 



approximation, and its derivation can be 
found in appendix A. 



i x < 1.4 v f (Y E -Y X ). (19) 

SAMPLING-TYPE FIRE DETECTORS 



The guidelines developed in the previ- 
ous sections apply directly to spot-type 
detectors, which may be located in fixed 
positions corresponding to the spacing 
recommended for a given entry. Con- 
sequently, for an entry of length & E , 
with a sensor requiring spacing £ x in 
that entry, the number of sensors (n) 
would equal £ E /£ X . 

An alternative to this type of system 
is a sampling-type fire detector. In- 
stead of having sensors located at fixed 
positions, a sampling-type detector has 
sampling ports connected to one single 
sensor via hollow-core tubing. Pumps are 
used to continuously pull samples of air 
from the sampling port locations to the 
detector where the samples are analyzed 
for combustion products. 

For this type of detector, the spacing 
guidelines cannot be applied directly to 
location of the sampling ports, because 
of the additional time that is required 
for the system to respond, owing to tube 
traveltimes and sequencing times at the 
detector station. In order to determine 
the required spacings for sampling ports 
for this type of sensor, the additional 
times must be included in the overall 
response time of the system (t s ). 

For a sampling-type detector, it is 
usually prudent to determine the number 
of sample ports (n) required to protect 
an entry of length £ E . To determine n, 
the time response of a sampling-type 
detector can be written as a function of 
n and other known variables. The time 



response of a sampling-type detector is 
given by 



t s = t D + t x + t £ + t 



seq > 



(21) 



where t$ = transport time of combus- 
tion product between sample 
ports; 

t x = time at which POC concentra- 
tion will reach the alarm 
threshold level (previously 
defined in equation 12); 

t£ = sample traveltime through 
the longest sampling tube; 7 



and 



•seq 



the time required by the de- 
tector to sequence through 
all sampling tubes , which 
is equal to the number of 
tubes (n) times the sampl- 
ing time per tube (t samp ). 



The total response time must be less 
than or equal to t T (equation 6) in order 
to satisfy the detection criterion. 
Since the sample port spacing (£ s ) equals 
£ E /n, the following equation must be 
satisfied: 



A E /n + v f (t £ + nt samp ) < l x , 



(22) 



where l x is the recommended spacing for 
category 1, 2, or 3 mine entries. 

Solving equation 22 for n yields 



See appendix B for derivation of t£ . 



a x -v f t £ ) - yu x -v f t £ ) 2 - 4 £ E t samp v f 

n= j- v (23) 

zt samp v f 

and is the defining equation for cate- For a category 4 mine entry (vf < 50 
gory 1, 2, or 3 mine entries. f t/min) , the resulting equation is 8 



Z 



^< 60H 1/2 [1.4 (Ye-Yx) " (t£ + nt samp )] 1 / 2 . (24) 

Equations 23 and 24 can be used to de- equal to £ E /n. Expressions for the tube 
termine the required number of sample traveltimes (t^) to be used in these two 
ports (n) for an entry of length £ E . The equations can be found in appendix B. 

spacing between sample ports (H s ) is then 

°See appendix A. 



10 



APPENDIX A. —DERIVATION OF LOW-FLOW SENSOR SPACINGS 



From data available in the literature, 1 
empirical expressions were derived for 
the maximum temperature difference (T max - 
T ) and maximum gas velocity (v max ) near 
the roof, as a function of roof height 
(H), fire heat release rate (Of), and 
radial distance (r) from the fire origin, 
for fires developing under static (no- 
flow) conditions. The respective ex- 
pressions for T max -T and v max are 



T - T = 

1 max • L o 



. 4.74 (Q f /r) 2/3 



v max is in ft/min; 
Qf is in Btu/min; 



(A-l) 



and v max = 15.0 Q f 1/3 H 1/2 /r 5/6 , (A-2) 



where T max and T are in ° F; 



Assuming that, under static conditions, 
the fire will grow at a rate less than or 
equal to the rate at the minimum velocity 
of Vf = 50 ft/min, equation 3 2 can be 
used to define the approximate fire 
growth rate: 



Qf - t 2 



When Qf = Q T , the approximate 
thermal alarm can be obtained: 



t T = 21.18 H 3/4 . 



(A-4) 



time to 



(A-5) 



By substituting equation A-4 into equa- 
tion A-2, the velocity (v max ) at any 
radial distance (r) becomes a function of 
time. By taking the integral average of 
v max , from t = to t = t j , the average 
velocity (v avg ) at any radial distance 
(r) can be obtained; that is, 



and 



H and r are in ft. 



These two expressions apply to radially 
expanding hot product gases, and, for a 
mine entry, hot gases can spread radially 
only until they reach the ribs of the 
entry. Once they reach the ribs, the hot 
gases will expand along the length of the 
entry, and at an increased rate. In view 
of this behavior, the following deriva- 
tion for POC sensor spacings , using these 
radially expanding expressions, should be 
viewed as conservative estimates. 

As before, the basis for comparison 
will be a series of ideal 160° F heat 
sensors spaced at intervals of 10 ft. 
Since the hot gases are free to expand 
radially under static conditions, the 
maximum distance they will travel before 
being detected will be one-half the spac- 
ing, or 5 ft. Using this value for r in 
equation A-l and assuming T = 65° F, the 
fire size at which T max = T a = 160° F can 
be obtained. It is 



Q T = 448.6 H 3/2 . 



(A-3) 



r c T 



v max (t) dt 



J o 



avg 



68.9 H 
r 5/6 ' 



(A-6) 



dt 



Equation A-6 defines the average veloc- 
ity at any radial distance (r) during the 
thermal alarm time interval (t T ). The 
average gas velocity (v ) that the hot 
gases will have in traversing a fixed 
distance (r ) is the integral average of 



avg 



from 



rr r 



r = o 



to 



r = r 



o > 



that is 



v aV q(r) d r 



ro 



413.4 H 
-7-5715—' 



(A-7) 



dr 



For ventilation velocities of 50 ft/min 
or less, the quantity A/vf will be limit- 
ed to a maximum value of 2, and from 
equation 18, the maximum transport time 



1 



'Alpert, R. L. Calculation of Response 
Time of Ceiling-Mounted Fire Detectors. 
Fire Technol . , v. 8, No. 3, August 1979, 
pp. 181-195. 



^Equation numbers without the A-prefix 
refer to equations occurring in the main 
text. 



11 



(to) is defined in terms of the param- 
eters y E and Y x by 

t D = 1.4 (Y E -Y X ). (A-8) 

For a POC fire sensor located at a dis- 
tance r from the fire, the average 
velocity (v ) required to traverse that 
distance in a time tp is 



equation A- 12 should be viewed as a con- 
servative approximation to the derived 
spacing. For example, with Y x = 15.1 (a 
CO sensor for 10 ppm above ambient) 
in an entry of H = 6 ft and W = 20 ft 
(Ye = 30.4), equation A-12 would require 
a spacing of 690 ft or less, while equa- 
tion A-ll would require a spacing of 756 
ft or less, a spacing about 10% larger. 



Vr, = 



_ L o _ 



tD 



1.4 (Yf-Yx)" 



(A-9) 



Since v from equation A-7 must equal v 
defined by equation A-9, the following 
expression can be obtained for r : 

r = 32.12 [H(y E -Y x )] 6 / 11 . (A-10) 

Equation A-10 defines the maximum radial 
expansion distance for a sensor (defined 
by Y x ) installed within an entry defined 
by H and Ye* Since the product gases 
expand both upstream and downstream, two 
sensors spaced at an interval of 2 r 
would be expected to respond at the same 
time to a fire located midway between 
them. Consequently, the maximum sensor 
spacing is defined by 

l x < 2r = 64.24 [H (Y E "Y X ) ] 6/1 1 • (A-ll) 

Assuming a minimum entry height of 
~3 ft and reasonable values of Ye - Y x 
lying between 5 and 30, the quantity H 
(Ye~Y x ) can be expected to lie between 15 
and 90, and equation A-ll can be approxi- 
mated by a more convenient expression 
given by 

i x < 72 [H(y E -Y x )] 1/2 . (A-12) 

If the ratio of equation A-ll to equation 
A-12 is taken, it can be shown that, for 
values of H(ye~Y x ) <12.3, equation A-ll 
will require a somewhat smaller spacing 
than that required by equation A-12. For 
values of H(ye - Y x ) >12.3, the spacing re- 
quired by A-12 will always be less than 
the spacing required by A-ll; thus, 



Consequently, for any entry in which 
the ventilation velocity is <50 ft/min, 
equation A-12 should be used to determine 
the appropriate spacing for a POC fire 
sensor. 

For a sampling-type fire detector, the 
maximum available transport time (tp) is 
given by 

t D = 1.4 (Y E "Y X ) - (t£ + nt samp ), (A-13) 

and the average velocity in traversing 
some distance r Q by 

. (A-14) 



1.4 (Ye-Y x ) " (t£ + nt samp ) 

Setting equation A-14 equal to equation 
A-7 and solving for r yields 

r = 27 H 6 /' 1 [1.4 (Ye"Y x ) 

- (t A + nt samp )] 6/n . (A-15) 

As before, the sample port spacing (£ s ) 
should be equal to 2 r , and, applying 
the same approximation as before (equa- 
tion A-12), the expression for the sample 
port spacing becomes 

£ s < 60 H 1/2 [1.4 (ye"Y x ) 

- (t £ + nt samp )] 1 / 2 . (A-16) 

For an entry of length, £ E , the sample 
port spacing equals H^/n, where n is the 
number of sample ports spaced at equal 
intervals. 



12 



APPENDIX B.— DERIVATION OF TUBE TRAVELIMES 



In general, the flow through each tube 
of a sampling-type detector should be 
laminar. In order to satisfy this con- 
straint, the Reynolds number should be 
less than or equal to 1,800. Then, 



Re= T^ l >™°> 



(B-l) 



where p = density of air = 0.075 lb/ 
ft 3 ; 

n = kinematic viscosity = 7.26 
x 10 _t+ lb/(ffmin); 

if = sample tube length, ft; 

d s = tube inside diameter, in; 

and tji = tube traveltime, min. 

Solving equation B-l for t£ yields 

t£ > 4.78 x 10 -3 if d s . (B-2) 

For sampling-type gas detectors (CO, 
CO2) there is an additional constraint on 
the size of tubing (d s ) that can be used 
for a given length (if). This constraint 
is related to the pumping requirements 
for the system, ' and is given by 



d s > 0.02 if 1/3 . 



(B-3) 



Substituting this expression into equa- 
tion B-2 yields 

ti > 9.56 x 10" 5 &,- 4/3 , (B-4) 

which defines the tube traveltime solely 
in terms of the tube length. Clearly, 
when if = £ max , the maximum tube length 
in the system, (t^) will have its great- 
est value. Then the maximum value of t£ 
is given by 

tg, > 9.56 x 10-5 £ max 4/3. (B _ 5) 

1 Litton, C. D. Design Criteria for 
Rapid Response of Pneumatic Monitoring 
Systems. BuMines IC 8912, in press; for 
information, contact C. D. Litton, Bureau 
of Mines, Pittsburgh, Pa. 



This is the expression to be used in 
equation 22 and 23 2 for a sampling-type 
gas detector. 

For a sampling-type smoke detector 
(SMP) there is a different constraint on 
the size of tubing (d s ) that can be used 
for a given length (if). This constraint 
is related to the losses of particles 
that can occur within a tube as the smoke 
is transported from the sample port to 
the detector. 3 The constraint is 



d s > 1.95 x 10" 4 if. 



-k 



(B-6) 



When if = £ max , the maximum tube travel- 
time is 



t £ > 9.32 x 10" 



i 2 



(B-7) 



This is the expression to be used for t^ 
in equations 22 and 23 for a sampling- 
type smoke detector. 

Both equations B-5 and B-7 indicate 
that the larger the value for £ max , the 
longer the tube traveltime (tjj,). Fur- 
ther, equations B-3 and B-6 indicate that 
as if increases , larger tube diameters 
(d s ) will be required. The values of 
i max and other sample tube lengths (if) 
depend upon the location of the detector 
station relative to the sample ports. 
The best location of the detector station 
is central to the location of the sample 
ports. For sample ports spaced at equal 
intervals (i s ) along an entry of length 
i^, and with the detector station located 
centrally with respect to the sample 
ports, the maximum tube length (H max ) is 
given by 



_ ^E~^s 



'max 



(B-8) 



Since i s = A E /n, i max can be rewritten as 



'max 



<m^- 



(B-9) 



^Equation numbers without the B-prefix 
refer to equations occurring in the main 
text. 

3 Work cited in footnote 1 . 




In general, it is sufficient to approx- 
imate the above equation by 



'max 



= 1/2 £ E 



(B-10) 



As a result, for applications in which 
the detector station can be located 
centrally with respect to the sample 
ports , the maximum tube traveltimes can 
be rewritten as 

t£ > 3.79 x 10" 5 U E ) 4/3 (B-ll) 

for sampling-type CO or CO2 detectors, 
and as 



13 



for sampling-type SMP detectors. 

For applications in which the detector 
station cannot be centrally located, the 
anticipated location of the detector 
relative to the farthest sample port 
will define £ max > an d t£ can De deter- 
mined from 
B-7. 



'max » 
either 



equation B-5 or 



It is important to note that all 
tubes must satisfy the size con- 
straints defined by either equation B-3 
or B-6. 



t£ > 2.33 x l(T 7 I- 2 



E > 



(B-12) 



i?rU.S. GOVERNMENT PRINTING OFFICE: 1983-605-015/10 



INT.-BU.OF MINES, PGH., PA. 26626 






P D 159 













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